About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

In-plane light propagation in two-dimensional (2D) photonic crystals (PCs) has been investigated by using the finite element method (FEM) in frequency domain. Conventionally, the band structures of 2D PCs were calculated by either the plane-wave expansion method (PWEM) or the finite difference time domain method. Here, we solve the eigenvalue equations for the band structures of the 2D PCs using the adaptive FEM in real space. We have carefully examined the convergence of this approach for the desired accuracy and efficiency. The calculated results show some discrepancies when compared to the results calculated by the PWEM. This may be due to the accuracy of the PWEM limited by the discontinuous nature of the dielectric functions. After acquiring the whole information of the dispersion relations within the irreducible Brillouin zone of the 2D PCs, the in-plane photon density of states for both the transverse electric (TE) and transverse magnetic (TM) modes can be calculated, accurately. For the case, the width of the complete band gap predicted by the FEM is much smaller, only about 65 % of that calculated by the PWEM. Therefore, the discrepancy in the prediction of complete band gaps between these two methods can be quite large, although the difference in band structure calculations is only a few percent. These results are relevant to the spontaneous emission by an atom, or to dipole radiation in two-dimensional periodic structures.

Tables (1)

Table 1. Paths, ranges of k∥ and ranges of phase changes, k∥ ’ R1 and k∥ ’ R2, for each of the segments required to traverse the boundary of the irreducible Brillouin zone for a square array and triangular array.

Metrics

Table 1.

Paths, ranges of k∥ and ranges of phase changes, k∥ ’ R1 and k∥ ’ R2, for each of the segments required to traverse the boundary of the irreducible Brillouin zone for a square array and triangular array.